My math book says two lines that are each perpendicular to the same
third line are not necessarily parallel to each other. How can that
be? They would not touch, and isn't that the definition of parallel
lines?

I'm puzzled by the ability of two fences with the same perimeter to have
very different areas inside them. I realize by LxW an 8' x 10' fence will
have more area than a 6' x 12' fence, but WHY? Both fences have 18'
surrounding them but different areas. Also does a circle or a square
conserve more area with identical perimeters?